Optimal Taxation Paper 7, Part IIb Dr Hamish Low

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Optimal TaxationPaper 7, Part IIbDr Hamish Low
Lecture 5
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Outline

• What factors matter for marginal tax rates?
• Numerical Simulations
• Distribution of ability
• Utilitarian vs Rawlsian SWF
• Compared to actual tax schedules

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Overall Tax Schedule
Imagine 3 groups of people labelled A, B and C
with low, medium and high incomes
Initial Tax Schedule
Increase marginal tax rate on range yA - yC
(Group B)
c
New Tax Schedule
y
Group A
Group B
Group C
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What factors matter?

• If large number of people at C, but few at B,
  then increase marginal tax rate on group B.
• (1) Distribution of population by gross income
  (ability)

f(ai)
y
5

• If large number of people at B, but few at A
  and C, then costly to increase marginal tax rate
  on group B.

f(ai)
y
6

• If compensated elasticity of labour supply at B
  is high then high welfare cost of marginal tax
  increase so need even more in group C to
  compensate.
• (2) Compensated elasticity of labour supply

Inelastic (low substitution)
j
c
y
7
Elastic (High substitution)
j
c
y
8

• Purpose is to transfer consumption to the lowest
  group, so need to know how inequality averse
• (3) Inequality Aversion

• Groups B and C lose utility, this reduces SW
• Group A gains because of revenue raised, this
  increases SW
• Monetary value of loss to B and C gt Revenue
  raised

• If government needs more revenue, then need
  higher marginal tax rates on everyone.
• (4) Revenue Requirement

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Summary

• Tax schedule depends on
• distribution of abilities
• compensated elasticities
• inequality aversion
• revenue requirement

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Numerical Results

• Assume distribution of abilities is log-normal

Observed distribution of gross-earnings is
log-normal so assuming that gross earnings
reflect ability
0.8
f(ai)
? 0.5
0.6
0.4
Need to know utility function and tax schedule to
pass from gross income to ability Certainly not
exogenous
0.2
? 1.0
0
ai
0
1
2
3
4
5
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• Non-redistributive government expenditure is 10
  of GDP

• Individual preferences described by Constant
  Elasticity of Substitution utility function
  (between leisure and consumption) ?

If Cobb-Douglas, ? 1.0

• Inequality aversion given by parameter ?

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Results
Negative ATR because universal benefit
Progressive tax Declining MTR but increasing ATR
Sensitivity to ?
MTR on 99 ? 0
Utilitarian Case
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MTR higher, but still declining
More Progressive ATR rise quicker
Sensitivity to ?
MTR on 99 ? 0
Moderate Egalitarian Case
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Very Progressive big payout if low income
MTR higher, but declines quickly at top
Rawlsian Case
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1.0
Rawlsian ? 0.5
MTR
Utilitarian ? 0.5
Utilitarian ? 1.0
0
0
1.0
Wage rate population deciles
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Summary

• Average tax rates rise with income marginal tax
  rates tend to decline
• Zero result on top earner is really only for the
  very top earner
• Declining MTR occurs with Rawlsian as well as
  Utilitarian SWF
• Numerical results sensitive to parameters
  particularly the compensated elasticity (of
  substitution)

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Actual Tax Schedules
Marginal tax rates (US)
MTR
Family of 4
40
20
ygross
50,000
100,000
-40
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Why do they differ?

• Cannot appeal to value judgements or to wrong
  elasticities
• Cost of unemployment missing from optimal tax
• Uncertainty high income individuals may be
  lucky
• Political constraints
• Only captures income taxes

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Changes over time mix of Direct and Indirect Tax

• Thatcher fallacy

Direct tax may be adjusted to the individual
characteristics of the tax payer Indirect tax
levied on transactions irrespective of identity
of tax payer
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Revenue Raised in UK ( of total revenue)
1979-1980
1999-2000
Income Tax
26
29
VAT
16
8
Excise Duties
20
13
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Thatcher Fallacy
Indirect taxes are a more efficient way to raise
revenue than income taxes because they have less
of an incentive effect on work The Economist,
9th October 1993
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Two goods (x and y) and hours of work (L)
Impose a uniform tax on the two goods
Equivalent to a linear tax on the wage rate
Spending power is identical under the two
taxes a 100 commodity tax equals a 50 income
tax
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A uniform commodity tax is equivalent to no
commodity tax and a suitably altered income tax.
Example here has no income tax, so equivalent
income tax is linear.
Revenue is redistributed as lump-sum so both
systems are progressive average tax increases
with income
Intuition the higher income person spends more,
so pays more tax
cutting income tax and raising VAT may not change
behaviour at all

• When will the switch change work incentives?

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Possible Explanations of Difference

• Change in tax base may be accompanied by change
  in progressivity
• Goods are taxed at different rates
• e.g. because consumption of a good reveals
  ability (redistribution)
• Intertemporal economy effect on savings
• People care about net income rather than
  spending power